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利用最优传输构建多属性数据的Copula图模型AI 解读

Abstract Motivated by modern data types such as images and multi-view data, the multi-attribute graphical model aims to uncover conditional independence structures among vector-valued nodes. Under the Gaussian assumption, such independence is encoded in blockwise zeros of the precision matrix. To relax the restrictive Gaussian assumption, we propose a semiparametric multi-attribute graphical model leveraging a newly introduced cyclically monotone copula. This copula treats…

利用大规模在线产品评分网络进行客户定位的模型式协同聚类AI 解读

Given the widely available online customer ratings on products, the individual-level rating prediction and clustering of customers and products are increasingly important for sellers to create targeting strategies for expanding the customer base and improving product ratings.However, the massive missing data problem is a significant challenge for modeling online product ratings.To address this issue, we propose a new co-clustering methodology based on a bipartite network…

通过弱条件期望实现随机对象的非线性全局 Fréchet 回归AI 解读

(2019) 691-719) emerges as a special case of our method by choosing a linear kernel. We require that the metric space for the predictor admits a reproducing kernel, while the intrinsic geometry of the metric space for the response is utilized to study the asymptotic properties of the proposed estimates. Numerical studies, including extensive simulations and a real application, are conducted to investigate the finite-sample performance.

Fréchet 回归的充分降维AI 解读

With the rapid development of data collection techniques, complex data objects that are not in the Euclidean space are frequently encountered in new statistical applications. Fréchet regression model (Petersen and Müller) provides a promising framework for regression analysis with metric space-valued responses. In this article, we introduce a flexible sufficient dimension reduction (SDR) method for Fréchet regression to achieve two purposes: to mitigate the curse of…

利用 Fisher 方法增强多因子资产定价模型检验功效AI 解读

Testing multi-factor asset pricing models is instrumental for asset pricing theory and practice. However, due to the accumulation of errors in estimating high-dimensional parameters, traditional quadratic-form tests such as the Wald test perform poorly against the sparse alternative hypothesis, i.e., a few mispriced assets. Fan et al. (2015b) introduced a powerful testing procedure by adding a power enhancement component to the Wald test statistic and proved power…

系数阈值化的稳健高维回归及影像数据应用AI 解读

It is important to develop statistical techniques to analyze high-dimensional data in the presence of both complex dependence and possible heavy tails and outliers in real-world applications such as imaging data analyses. We propose a new robust high-dimensional regression with coefficient thresholding, in which an efficient nonconvex estimation procedure is proposed through a thresholding function and the robust Huber loss. The proposed regularization method accounts for…

高维协方差矩阵的Fisher合并概率检验AI 解读

Testing large covariance matrices is of fundamental importance in statistical analysis with high-dimensional data. In the past decade, three types of test statistics have been studied in the literature: quadratic form statistics, maximum form statistics, and their weighted combination. It is known that quadratic form statistics would suffer from low power against sparse alternatives and maximum form statistics would suffer from low power against dense alternatives. The…

离散数据的加性图模型AI 解读

We introduce a nonparametric graphical model for discrete node variables based on additive conditional independence. Additive conditional independence is a three-way statistical relation that shares similar properties with conditional independence by satisfying the semi-graphoid axioms. Based on this relation we build an additive graphical model for discrete variables that does not suffer from the restriction of a parametric model such as the Ising model. We develop an…

高维均值向量与协方差矩阵的功效增强联合检验及基因集应用AI 解读

Power-enhanced tests with high-dimensional data have received growing attention in theoretical and applied statistics in recent years. Existing tests possess their respective high-power regions, and we may lack prior knowledge about the alternatives when testing for a problem of interest in practice. There is a critical need of developing powerful testing procedures against more general alternatives. This article studies the joint test of two-sample mean vectors and…

高维成分数据的稳健协方差估计及销售数据应用AI 解读

Compositional data arises in a wide variety of research areas when some form of standardization and composition is necessary. Estimating covariance matrices is of fundamental importance for high-dimensional compositional data analysis. However, existing methods require the restrictive Gaussian or sub-Gaussian assumption, which may not hold in practice. We propose a robust composition adjusted thresholding covariance procedure based on Huber-type M-estimation to estimate the…

利用高维预测变量进行充分预测的逆矩方法AI 解读

Summary We consider forecasting a single time series using a large number of predictors in the presence of a possible nonlinear forecast function. Assuming that the predictors affect the response through the latent factors, we propose to first conduct factor analysis and then apply sufficient dimension reduction on the estimated factors to derive the reduced data for subsequent forecasting. Using directional regression and the inverse third-moment method in the stage of…

因子数增长时充分预测的非参数估计与共形推断AI 解读

The sufficient forecasting (SF) provides a nonparametric procedure to estimate forecasting indices from high-dimensional predictors to forecast a single time series, allowing for the possibly nonlinear forecasting function. This article studies the asymptotic theory of the SF with a diverging number of factors and develops its predictive inference. First, we revisit the SF and explore its connections to Fama–MacBeth regression and partial least squares. Second, with a…

利用因子模型进行充分预测AI 解读

We consider forecasting a single time series when there is a large number of predictors and a possible nonlinear effect. The dimensionality was first reduced via a high-dimensional factor model implemented by the principal component analysis. Using the extracted factors, we develop a novel forecasting method called the sufficient forecasting, which provides a set of sufficient predictive indices, inferred from high-dimensional predictors, to deliver additional predictive…

transnormal 模型下的多任务分位数回归AI 解读

We consider estimating multitask quantile regression under the transnormal model, with focus on high-dimensional setting. We derive a surprisingly simple closed-form solution through rank-based covariance regularization. In particular, we propose the rank-based ℓ1 penalization with positive-definite constraints for estimating sparse covariance matrices, and the rank-based banded Cholesky decomposition regularization for estimating banded precision matrices. By taking…

折叠凹惩罚估计的强 oracle 最优性AI 解读

Folded concave penalization methods have been shown to enjoy the strong oracle property for high-dimensional sparse estimation. However, a folded concave penalization problem usually has multiple local solutions and the oracle property is established only for one of the unknown local solutions. A challenging fundamental issue still remains that it is not clear whether the local optimum computed by a given optimization algorithm possesses those nice theoretical properties. To…

大型协方差矩阵的正定 ℓ1 惩罚估计AI 解读

The thresholding covariance estimator has nice asymptotic properties for estimating sparse large covariance matrices, but it often has negative eigenvalues when used in real data analysis. To fix this drawback of thresholding estimation, we develop a positive-definite ℓ1-penalized covariance estimator for estimating sparse large covariance matrices. We derive an efficient alternating direction method to solve the challenging optimization problem and establish its convergence…

高维非正态变换图模型的正则化秩估计AI 解读

A sparse precision matrix can be directly translated into a sparse Gaussian graphical model under the assumption that the data follow a joint normal distribution. This neat property makes high-dimensional precision matrix estimation very appealing in many applications. However, in practice we often face nonnormal data, and variable transformation is often used to achieve normality. In this paper we consider the nonparanormal model that assumes that the variables follow a…

稀疏 Ising 模型的非凹惩罚复合条件似然估计AI 解读

The Ising model is a useful tool for studying complex interactions within a system. The estimation of such a model, however, is rather challenging, especially in the presence of high-dimensional parameters. In this work, we propose efficient procedures for learning a sparse Ising model based on a penalized composite conditional likelihood with nonconcave penalties. Nonconcave penalized likelihood estimation has received a lot of attention in recent years. However, such an…